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S. Shiakolas R ─ G H C k1 = R s 2 + (2 + k1k 2 )s + k1 ME 5303 Classical Methods of Control Systems – Analysis & Synthesis C Type of system = Type 1 GH = k1 s1 (s + 2 ) (1 + k2 s ) Assume FVT applicable ess = lim sE ( s ) = lim s(1 − TF )R s →0 s →0 ⎛ ⎞ + + s k k 2 1 2 ⎟ = lim A⎜ s → 0 ⎜⎝ s 2 + (2 + k1k 2 )s + k1 ⎟⎠ A(2 + k1k 2 ) 10 ess = < A k1 100 © 2005 P. S. 1 k1 © 2005 P. S. 14) 4 © 2005 P. S. Shiakolas ME 5303 Classical Methods of Control Systems – Analysis & Synthesis STABILITY STABLE t Im NEUTRAL Re t UNSTABLE t © 2005 P.

T. variable z X s+a = U s 2 + 2ξωn s + ωn2 From the block diagram, Z X 1 = = s+a & 2 2 U s + 2ξωn s + ωn Z Z ⇒ &z& + 2ξωn z& + ωn2 z = u U Converting into state space, φ =z φ = φ& = z& 1 © 2005 P. S. Shiakolas 2 2 ME 5303 Classical Methods of Control Systems – Analysis & Synthesis φ&1 = 0φ1 + 1φ2 + 0u φ&2 = −ωn2φ1 − 2ξωnφ2 − 1u ⎛ φ&1 ⎞ ⎡ 0 ⎜ ⎟=⎢ ⎜ φ& ⎟ ⎢− ω 2 ⎝ 2⎠ ⎣ n ⎤ ⎛ φ1 ⎞ ⎛ 0 ⎞ ⎥⎜ ⎟+ ⎜ ⎟u − 2ξωn ⎥⎦ ⎜⎝ φ2 ⎟⎠ ⎜⎝ − 1⎟⎠ 1 X ⇒ x = z& + az Z x = aφ1 + 1φ2 + 0u © 2005 P. S. Shiakolas ME 5303 Classical Methods of Control Systems – Analysis & Synthesis FEEDBACK CONTROL SYSTEM CHARACTERISTICS STATE SPACE BLOCK DIAGRAM TRANSFER FUNCTION © 2005 P.

S. Shiakolas ME 5303 Classical Methods of Control Systems – Analysis & Synthesis ROUTH TABLE Power Coefficients sn an an − 2 an − 4 s n −1 an −1 an −3 an − 5 sn−2 b1 b2 s n −3 c1 c2 b3 M s0 © 2005 P. S.

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